order	48
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = D₃×B(4,𝔽₂) (order 384) · Inn(G) = C₂×D₃ · Out(G) = #120
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₂×Dic₆
unambiguous semidirect product	(C₂×C₃)⋊Q₈

Splittings

C₃ ⋊ C₂×Q₈

38 conjugacy classes of subgroups.

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 3 generators on 13 points:

(3,4,5)(6,8,9,13)(7,10,11,12);(1,2)(4,5)(6,7,9,11)(8,12,13,10);(1,2)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(48, 34);